Evaluate 3(x+1)^2

$3 {(x + 1)}^{2}$

Rewrite ${(x + 1)}^{2}$ as $(x + 1) (x + 1)$ .

$3 ((x + 1) (x + 1))$

Expand $(x + 1) (x + 1)$ using the FOIL Method.

Apply the distributive property.

$3 (x (x + 1) + 1 (x + 1))$

Apply the distributive property.

$3 (x \cdot x + x \cdot 1 + 1 (x + 1))$

Apply the distributive property.

$3 (x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1)$

$3 (x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$3 (x^{2} + x \cdot 1 + 1 x + 1 \cdot 1)$

Multiply $x$ by $1$ .

$3 (x^{2} + x + 1 x + 1 \cdot 1)$

Multiply $x$ by $1$ .

$3 (x^{2} + x + x + 1 \cdot 1)$

Multiply $1$ by $1$ .

$3 (x^{2} + x + x + 1)$

$3 (x^{2} + x + x + 1)$

Add $x$ and $x$ .

$3 (x^{2} + 2 x + 1)$

$3 (x^{2} + 2 x + 1)$

Apply the distributive property.

$3 x^{2} + 3 (2 x) + 3 \cdot 1$

Simplify.

Multiply $2$ by $3$ .

$3 x^{2} + 6 x + 3 \cdot 1$

Multiply $3$ by $1$ .

$3 x^{2} + 6 x + 3$

$3 x^{2} + 6 x + 3$

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